What question did this study set out to answer?

The aim is to establish a dynamical foundation for models of anomalous diffusion using fractional Brownian motion with random parameters.

Limit theorems for the dynamical foundation of the fractional Brownian motion and related models of anomalous diffusion with random diffusion coefficient and time-dependent random Hurst parameter

View Full Paper

Ask AI

Bookmark

Authors

Analysis demonstrates the behavior of test-particle diffusion in complex environments, suggesting new modeling approaches.

The aim is to establish a dynamical foundation for models of anomalous diffusion using fractional Brownian motion with random parameters.
Development of a dynamical system for test-particle motion among varying mass Brownian particles.
Application of underdamped Langevin equations to describe the system.
Exploration of momentum and energy conservation principles.
Limiting behavior of the test-particle diffusion as N approaches infinity.
Diffusion of the test-particle is represented by a non-Markovian Gaussian process.
Covariance function is influenced by the mass distribution of surrounding particles.
Specific mass distributions yield fractional Brownian motion and other anomalous diffusion models.
Generalized Kolmogorov-Fokker-Planck equations correspond to the discussed processes.

Bender et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark